Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay

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2 Module 5: Lecture -1 on Stability of Slopes

3 Contents Stability analysis of a slope and finding critical slip surface; Sudden Draw down condition, effective stress and total stress analysis; Seismic displacements in marginally stable slopes; Reliability based design of slopes, Methods for enhancing stability of unstable slopes.

4 Contents of this lecture Types of slopes Failure types Causes of slope failures Analysis of slopes by using LE methods Comparison Concluding remarks

5 Application of shear strength theory Earth pressure theories Stability analysis of slopes Infinite slopes Slope that extends over a long distance and the conditions remain identical along some surface or surfaces for quite some distance. Finite slopes Slope that connect land at one elevation to land that is not far away but is at different elevation. Can also exist in nature and man-made.

6 Type of slopes Slopes Natural Hill side and valleys Coastal and river cliffs Man-made Cuttings and embankments for highways and rail roads Earth and ash pond dams Temporary excavations Waste heaps (landfill slopes) Landscaping for site development

7 Types of slope failure R R Circular Non-circular

8 Types of slope failure Translational slip

9 Types of slope failure Compound slip Rigid stratum

10 Block movement Resisting force F R : µ s N W W Disturbing force F D : F F 1 F 1 F FS = F F R D µ k N N µ s N N As long as µ s N > F --- block is said to be stationary

11 Causes of slope failure Gravity Seepage Earthquake Erosion Geological features Construction activities

12 Typical slope failures

13 Typical slope failures September 15, 2004 Courtesy: Geological natural hazards

14 Landslide damage adjacent to a residential structure Courtesy: North Carolina Geological Survey

15 Typical slope failures

16 Highway slope failure at Krishnabhir, Tribhuwan highway Nepal (Aryal, 2003)

17 Typical sacrificial slope failure in highway embankment (After Loher et al. 2002)

18 Uttarakand (2013)

19 Landslide in Chongqing and Hong Kong After Kwong et al. 2004

20 Effect of raising GWT

21 Aerial view of Waste slide on March 16, 1996 [USA] Lateral displacements upto 275 m and vertical displacements upto 61 m 1.2 million m 3 of waste After Eid et al. (2000)

22 Aerial view of landfill on Feb. 6, 1996 Stark et al. (2000)

23 Slope failures depend on Slope Failure Soil type Soil stratification Ground water Seepage Slope geometry

mass travels long distances before coming to rest.

24 Types of Slope Failure Translational Slide Failure of a slope along a weak zone of a soil Sliding mass travels long distances before coming to rest. Common in coarsegrained soils. Thin layer of weak soil

25 Types of Slope Failure Rotational slide Common in homogenous fine-grained soil It has its point of rotation on an imaginary axis parallel to the slope There are three types of rotational failure: Base slide Toe slide Slope slide

26 Rotational slide Base slide Occurs by an arc engulfing the whole slope. A soft soil layer resting on a stiff layer of soil is prone to base slide

27 Rotational slide Toe slide The failure surface passes through the toe of the slope.

28 Rotational slide Slope slide The failure surface passes through the slope

29 Flow slide Occurs when internal and external conditions force a soil to behave as a viscous fluid and flow down, spreading in all directions. Multiple failure surfaces occur and change continuously as flow proceeds. Occurs in dry and wet soils.

30 Block and wedge slide Occurs when a soil mass is shattered along joints, seams, fissures and weak zones by forces emanating from adjacent soils. The shattered mass moves as blocks and wedges down the slopes.

31 Falls Simple detachment of rock mass from its parent body The process is only gravity governed. Rock falls

32 Causes of Slope Failure Erosion Water and wind continuously erode slopes. Erosion changes the geometry of the slopes, resulting in a slope failure or a landslide. Steepening of slope by erosion

33 Causes of Slope Failure Erosion: Rivers and streams continuously scour their banks undermining their natural or man-made slopes. Scour by rivers and streams

34 Causes of Slope Failure Rainfall: Long periods of rainfall saturate, soften, and erode soils. Water enters into existing cracks and may weaken underlying soil layers, leading to failure, (for example, mud slides)

35 Causes Of Slope Failure Earthquakes: Earthquakes induce dynamic forces especially dynamic shear forces that reduce the shear strength and stiffness of the soil.

36 Earthquakes: Pore water pressures in saturated coarse-grained soils could rise to a value equal to the total mean stress and cause these soils to behave like viscous fluids. This phenomenon is known as dynamic liquefaction. Structures founded on these soils would collapse. The quickness in which the dynamic forces are induced prevents even coarse grained soils from draining the excess pore water pressures. Thus, failure in a seismic event often occurs under undrained conditions.

37 Causes of Slope Failure Geological features: Many failures commonly result from unidentified geological features. Soil stratification

38 Causes of Slope Failure External Loading: Loads placed on the crest of a slope add to gravitational load and may cause slope failure. Overloading at the crest of the slope

39 Construction activities: Construction activities near the toe of an existing slope can cause failure because lateral resistance is removed. Slope failures due to construction activities is divided into two cases: Excavated slopes. Fill slopes. Excavation at toe of the slope

40 Excavated slopes: When excavation occurs, the total stresses are reduced and negative pore pressures are generated. With time the negative pore pressures dissipate, causing a decrease in effective stresses and consequently lowering the shear strength of the soil. If slope failures occur, they take place after construction is completed.

41 Fill slopes: Fill slopes are common in embankment construction. If the foundation soil is saturated, then positive pore water pressures are generated from the weight of the fill and the compaction process. The effective stress decrease and consequently shear strength decreases. Slope failures in slope are likely to occur during or immediately after construction.

42 Factors contributing to instability of soil slopes Factors that contribute to high shear stress: i) Removal of lateral support a) Erosion bank cutting by streams and rivers b) Human agencies cuts, canals, pits, etc., ii) Surcharge a) Natural agencies Weight of snow, ice and rain water b) Human agencies Fills, buildings, etc., iii) Transitory earth stresses Earthquakes iv) Removal of underlying support a) Sub aerial weathering solutioning by ground water b) Subterranean erosion piping c) Human agencies mining v) Lateral pressures water in vertical cracks; freezing water in cracks; root wedging After Gray and Leiser (1982)

43 Factors contributing to instability of soil slopes Factors that contribute to low shear strength i) Initial state ii) iii) ii) a) Composition inherently weak materials After Gray and Leiser (1982) b) Texture loose soils, metastable grain structures c) Gross structure faults, joining, bedding, planes, varying, etc., Changes due to weathering and other physicochemical reactions - Frost action and thermal expansion, Hydration of clay minerals, Drying and cracking, Leaching Changes in inter-granular forces due to pore water - Seepage pressure of percolating ground water, loss in capillary tension upon saturation, buoyancy in saturated state. Changes in structure Fissuring of pre-consolidated clays due to release of lateral restraint; Grain structure collapse upon disturbance.

44 General Assumptions: Slope Stability Analysis The failure can be represented as a two dimensional problem. The sliding mass moves as a rigid body and the deformations of the sliding mass has no significant effects on the analysis. The properties of soil mass are isotropic and shear resistance along failure surface remains same independent of the orientation of the failure surface. The analysis is based on limit equilibrium method.

45 Infinite Slope Stability Analysis

46 Examples of slopes which can be infinite slopes Ore or sand stock piling by dropping from a chute Embankment formed by end dumping from a truck Natural slopes formed in granular materials where the critical failure mechanism is shallow sliding or surface ravelling Natural slopes formed in cohesive soils with great extent or weak cohesive material on ledge Slopes in residual soils where a relatively thin layer of weathered soil overlies a firmed soil or rock

47 Analysis of infinite slopes Assumptions: Soil is homogenous. The stress and soil properties on every vertical plane are identical; On any plane parallel to the slope stresses and soil properties are identical. h w b β z Failure surface Failure in such slope takes place due to sliding of the soil mass along a plane parallel to the slope at a certain depth.

48 Analysis of infinite slopes b D Weight of segment ABCD W = γzb(1) Tangential stress τ down the slope A W z τ = Normal stress σ within the segment σ = γzbsin β = γz sin β cos β b / cos β γzb cos β 2 = γz cos β b / cos β B T N C Pore water pressure u on the slip surface u = 2 ( z ) γ cos β h w w

49 Analysis of infinite slopes Normal effective stress σ = = γ = 2 z cos β ( z hw ) γ w 2 ( γz γ z + γ h ) cos β w w w cos 2 β Shearing strength τ f at the base of segment τ = c + σ tanφ f Factor of safety can be defined as: FS = τ f τ For the general case: FS = c + 2 tanφ cos β γz sin β cos β ( γz γ z γ h ) w + w w

50 Analysis of infinite slopes Special cases Case - A FS = tan φ tan β For the critical case FS = 1 β = φ For β < φ τ < τ f Slope is stable Dry Cohesion-less soil (independent of depth of slope) For β > φ τ > τ f Slope would have already failed at all depths. c = 0; h = w FS of an infinite slope with a cohesion-less soil is independent of the depth of failure plane. Slope is just stable τ z Mohr failure envelope (σ f, τ f ) β φ (σ, τ) σ

51 Analysis of infinite slopes Case B Saturated cohesion-less slope γ tan φ FS = γ tan β c w = 0 ; h = 0 Factor of safety of a saturated cohesion-less slope is about ½ for a slope without saturation. Case - C For a c - φ soil h w = 0 FS = 2 c + tanφ cos β γz sin β cos β ( γ z)

52 Analysis of infinite slopes Case - C For a c - φ soil h w = 0 FS = Assuming FS = 1 2 c + tanφ cos β γz sin β cos β z = h c ( γ z) Stability number h c = c sec 2 β γ γ tan β tanφ γ c γ h c = γ tan β tanφ γ 2 sec β For c-φ soils there is a limiting depth for stability

53 Analysis of infinite slopes Case - C For a c - φ soil τ Mohr failure envelope For β 1 < φ τ < τ f τ = τ f φ For β 2 > φ τ = τ f (σ f, τ f ) The depth at which τ = τ f is called the critical depth h c β 1 β 2 (σ, τ) For this depth slope is just stable σ

Slope Stability. loader

Slope Stability. loader Slope Stability Slope Stability loader Lower San Fernando Dam Failure, 1971 Outlines Introduction Definition of key terms Some types of slope failure Some causes of slope failure Shear Strength of Soils